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Welcome to Thetabruv.com.
I use this space to share the theoretical and practical foundations of a few strategies for capturing the volatility risk premium (VRP). I became interested in the subject in 2019, after a decade or so of passive investing, when I started asking myself whether a retail investor could go beyond building a portfolio of ETFs.
Over the years I collected quite a lot of material, and I decided to structure it into this site — for myself, and for the friends and acquaintances I end up discussing it with. It is therefore a living repository rather than a finished work: nobody should be surprised by corrections and re-editions.
These pages are quite far from the personal-finance topics you are used to seeing, and they are not for everyone: I am well aware these are niche subjects. If you find the strategies needlessly complicated and risky, that is perfectly fine! I hope you can at least take away some new information, and that you appreciate the effort to bring something different to the financial-education space.
The site is organized into four sections, plus this introductory page.
In the first section, Derivatives, I quickly cover the main concepts behind futures and options, which are the instruments used in the strategies. It is not meant to be a complete treatment, and I expect you to be already familiar with the basics (plenty of resources are available online otherwise). Here I give a quick overview of some characteristics and false myths of derivatives, and of how they are priced by theoretical models and by the market. I then introduce the protagonist of the story, the volatility risk premium (VRP), and how it can be captured without giving up any of the other risk premia in the portfolio — first of all the equity risk premium (ERP) and the term risk premium (TRP), that is, stocks and bonds. The core idea is this: just as the ERP is the price that convinces someone to hold the aggregate risk of businesses, and the TRP the price for carrying duration, the VRP is the price that convinces the marginal seller of insurance to stay short a negatively skewed risk, against a structurally excessive demand for protection. Without that premium, the supply of options would collapse: nobody sells insurance at actuarial fair value. Finally, I cover the concept of capital efficiency and why it is preferable to collect VRP by stacking it on top of a portfolio that already accrues ERP and TRP. Instead of selling Cash Secured Puts (CSP), I use the portfolio’s purchasing power to sell Naked Puts (NP) on margin, with moderate leverage that carries no risk of ruin. I also show which portfolio I stack volatility on: I prefer to keep the portion covering the VaR in low-volatility products (bonds, for the time being), since volatility selling has the unwelcome property of being correlated with equities at the worst possible moment — during violent equity corrections.
In the second section, Risk Management, I expand on managing risk in a margin portfolio that uses derivatives. It starts from the definition of risk and moves on to measurement techniques (volatility, Sharpe and information ratio, VaR, stress tests), with a warning that runs through the whole site: metrics based on volatility alone make volatility-selling strategies look systematically very profitable, which is why they must be paired with tail measures, given the negative skewness. I devote an entire page to tail risk — the protagonist of these strategies — how it arises and how it is managed. The section closes with my reflections on ergodicity and on why even a volatility-selling strategy can be made ergodic: it all comes down to position sizing (how much capital to allocate to each trade) and risk management (stop-losses, loss limits and hedging) to avoid irreversible losses — that is, the risk of ruin.
The third section, Strategies, covers my two favourite volatility-selling strategies: tail risk protection selling (TRPS) and delta-hedged convexity selling (DHCS). The first has been extensively documented by Big ERN on his site Early Retirement Now, which I recommend reading. In its pure form, it boils down to selling deep-OTM puts on the S&P 500 index with a one-day maturity (1DTE), so as to collect roughly 252 nearly independent positions per year from which to extract VRP. The second is based on an AQR paper by Israelov that identifies the part of the option surface that maximizes return per unit of stress: it involves selling puts on the S&P 500 as well, but only slightly OTM (2-3%) and with roughly 30 days to expiry. The position is then hedged by selling index futures in an amount equal to the delta, so as to isolate the VRP alone. The hedge is dynamic and must be recalculated at the end of each day. Near expiry the positions are rolled (existing ones are closed and new ones opened), to avoid the gamma explosion close to expiration.
A separate chapter is devoted to the edge (competitive advantage) of these strategies: if they are so profitable, why don’t market makers and prop trading firms like Citadel, Susquehanna and Jane Street take all the profit for themselves? The question is ill-posed, though, because it assumes a model where retail competes with the market maker in a zero-sum game in which somebody wins and somebody loses. In reality, the reference model is the reinsurance business: an insurance company (the cedent, represented here by the market makers) transfers part of the risks it has underwritten to a reinsurer (whoever runs short-vol strategies, such as retail traders and hedge funds). In exchange, the cedent also passes along a portion of the premiums collected. The purpose is risk management: an insurer that has sold thousands of home policies in Florida (or SPX puts) would be exposed to catastrophic losses from a single hurricane in that area (a quick crash of the S&P 500). By transferring part of that risk, it protects its balance sheet and lowers its inventory risk. But why transfer the risk instead of simply not underwriting it in the first place? Because market makers must, by definition, provide liquidity to the market, and they prefer to slow demand down by raising the price of insurance (and hence the profitability of selling it) and possibly reselling it, in order to stay as market-neutral as possible (or with an acceptable inventory VaR). When I sell a put, I enter the market makers’ value chain as a supplier, not as a competitor: my very existence is in the market makers’ interest, because I allow a more flexible management of risk — and that is why they pass part of their profits back to me.
The fourth section, Execution, is where I get practical: although these are low-frequency strategies that take at most about ten minutes a day when run manually, I describe a personal project in which I automated them. I start from what features the broker must have, and move on to the hardware setup and the software architecture of the Python bot — my personal vibe coding project — that runs them for me and that I monitor remotely through messaging and email. After all, what could possibly go wrong in letting a bot that sells puts on margin operate a live trading account from a headless Chinese mini PC at home?
Happy reading.
Theta Bruv